What one of the following is correct ?
`(1+cos67(1^(@))/(2))(1+cos112(1^(@))/(2))`is

Options

A. an irrational number and is greater than 1
B. a rational number but not an integer
C. an integer
D. an irrational number and is less than 1

Answer

D

Explanation

The given expression `(1+cos67(1^(@))/(2))(1+cos112(1^(@))/(2))`
Can also be writters as :
`=(1+cos67(1^(@))/(2))(1-cos67(1^(@))/(2))`
`=1cos^(2)67^(@)(1^(@))/(2)=sin^(2)67(1^(@))/(2)`
`=(1-cos135^(@))/(2)=(sqrt(2)+1)/(2sqrt(2))" " (because sin^(2)A=(1-cos2A)/(2))`
Which is an irrational and is less than 1.